Constant-pressure Monte Carlo: Difference between revisions
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m (correction of first eq.) |
m (cosmetic changes) |
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The [[weighting function]], ''w'', is given by (Ref 1 Eq. 2) | The [[weighting function]], ''w'', is given by (Ref 1 Eq. 2) | ||
:<math>w \simeq c \frac{V^N}{N!} \exp \left | :<math>w \simeq c \frac{V^N}{N!} \exp \left\{ -\beta [ U(q^N) +pV ] \right\} </math> | ||
for a change in volume, <math>\Delta V</math>, one has | for a change in volume, <math>\Delta V</math>, one has | ||
Revision as of 10:37, 24 February 2009
In constant-pressure Monte Carlo a trial change in the volume becomes one of the Monte Carlo moves. The weighting function, w, is given by (Ref 1 Eq. 2)
![{\displaystyle w\simeq c{\frac {V^{N}}{N!}}\exp \left\{-\beta [U(q^{N})+pV]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e273fa3bb7762d9238306b389bd1d7b4b4815215)
for a change in volume, , one has
![{\displaystyle r={\frac {w_{\rm {new}}}{w_{\rm {old}}}}=\exp \left[-\beta \left(\Delta U+p\Delta V-Nk_{B}T\ln {\frac {V+\Delta V}{V}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee39f2e32f0d105ac442a447e3b0f59b762c73f3)
If then the move is accepted, and if then r is compared with a random number . If then the move is accepted.
